Efficient Location of Resources in Cylindrical Networks
The location of resources in a network satisfying some optimization property is a classical combinatorial problem that can be modeled and solved by using graphs. Key tools in this problem are the domination-type properties, which have been defined and widely studied in different types of graph model...
| Main Authors: | , , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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MDPI
2020
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/7349 |
| _version_ | 1789406455337582592 |
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| author | Carreño, José Juan Martínez García, José Antonio Puertas González, María Luz |
| author_facet | Carreño, José Juan Martínez García, José Antonio Puertas González, María Luz |
| author_sort | Carreño, José Juan |
| collection | DSpace |
| description | The location of resources in a network satisfying some optimization property is a classical combinatorial problem that can be modeled and solved by using graphs. Key tools in this problem are the domination-type properties, which have been defined and widely studied in different types of graph models, such as undirected and directed graphs, finite and infinite graphs, simple graphs and hypergraphs. When the required optimization property is that every node of the network must have access to exactly one node with the desired resource, the appropriate models are the efficient dominating sets. However, the existence of these vertex sets is not guaranteed in every graph, so relaxing some conditions is necessary to ensure the existence of some kind of dominating sets, as efficient as possible, in a larger number of graphs. In this paper, we study independent [1,2] -sets, a generalization of efficient dominating sets defined by Chellali et al., in the case of cylindrical networks. It is known that efficient dominating sets exist in very special cases of cylinders, but the particular symmetry of these graphs will allow us to provide regular patterns that guarantee the existence of independent [1,2] -sets in every cylinder, except in one single case, and to compute exact values of the optimal parameter, the independent [1,2] -number, in cylinders of selected sizes. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-7349 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2020 |
| publisher | MDPI |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-73492023-04-12T19:37:23Z Efficient Location of Resources in Cylindrical Networks Carreño, José Juan Martínez García, José Antonio Puertas González, María Luz cartesian product of graphs efficient domination tropical matrix algebra The location of resources in a network satisfying some optimization property is a classical combinatorial problem that can be modeled and solved by using graphs. Key tools in this problem are the domination-type properties, which have been defined and widely studied in different types of graph models, such as undirected and directed graphs, finite and infinite graphs, simple graphs and hypergraphs. When the required optimization property is that every node of the network must have access to exactly one node with the desired resource, the appropriate models are the efficient dominating sets. However, the existence of these vertex sets is not guaranteed in every graph, so relaxing some conditions is necessary to ensure the existence of some kind of dominating sets, as efficient as possible, in a larger number of graphs. In this paper, we study independent [1,2] -sets, a generalization of efficient dominating sets defined by Chellali et al., in the case of cylindrical networks. It is known that efficient dominating sets exist in very special cases of cylinders, but the particular symmetry of these graphs will allow us to provide regular patterns that guarantee the existence of independent [1,2] -sets in every cylinder, except in one single case, and to compute exact values of the optimal parameter, the independent [1,2] -number, in cylinders of selected sizes. 2020-01-16T09:33:47Z 2020-01-16T09:33:47Z 2018-01-10 info:eu-repo/semantics/article 2073-8994 http://hdl.handle.net/10835/7349 en https://www.mdpi.com/2073-8994/10/1/24 Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess MDPI |
| spellingShingle | cartesian product of graphs efficient domination tropical matrix algebra Carreño, José Juan Martínez García, José Antonio Puertas González, María Luz Efficient Location of Resources in Cylindrical Networks |
| title | Efficient Location of Resources in Cylindrical Networks |
| title_full | Efficient Location of Resources in Cylindrical Networks |
| title_fullStr | Efficient Location of Resources in Cylindrical Networks |
| title_full_unstemmed | Efficient Location of Resources in Cylindrical Networks |
| title_short | Efficient Location of Resources in Cylindrical Networks |
| title_sort | efficient location of resources in cylindrical networks |
| topic | cartesian product of graphs efficient domination tropical matrix algebra |
| url | http://hdl.handle.net/10835/7349 |
| work_keys_str_mv | AT carrenojosejuan efficientlocationofresourcesincylindricalnetworks AT martinezgarciajoseantonio efficientlocationofresourcesincylindricalnetworks AT puertasgonzalezmarialuz efficientlocationofresourcesincylindricalnetworks |